Depth From Defocus: A Real Aperture Imaging Approach

TLDR: A Partial Derivatives of Various Quantities in CRB, a MAP-MRF approach to Depth Recovery and Restoration using MRF Models.

Abstract: 1 Passive Methods for Depth Recovery.- 1.1 Introduction.- 1.2 Different Methods of Depth Recovery.- 1.2.1 Depth from Stereo.- 1.2.2 Structure from Motion.- 1.2.3 Shape from Shading.- 1.2.4 Range from Focus.- 1.2.5 Depth from Defocus.- 1.3 Difficulties in Passive Ranging.- 1.4 Organization of the Book.- 2 Depth Recovery from Defocused Images.- 2.1 Introduction.- 2.2 Theory of Depth from Defocus.- 2.2.1 Real Aperture Imaging.- 2.2.2 Modeling the Camera Defocus.- 2.2.3 Depth Recovery.- 2.2.4 Sources of Errors.- 2.3 Related Work.- 2.4 Summary of the Book.- 3 Mathematical Background.- 3.1 Introduction.- 3.2 Time-Frequency Representation.- 3.2.1 The Complex Spectrogram.- 3.2.2 The Wigner Distribution.- 3.3 Calculus of Variations.- 3.4 Markov Random Fields and Gibbs Distributions.- 3.4.1 Theory of MRF.- 3.4.2 Gibbs Distribution.- 3.4.3 Incorporating Discontinuities.- 4 Depth Recovery with a Block Shift-Variant Blur Model.- 4.1 Introduction.- 4.2 The Block Shift-Variant Blur Model.- 4.2.1 Estimation of Blur.- 4.2.2 Special Cases.- 4.3 Experimental Results.- 4.4 Discussion.- 5 Space-Variant Filtering Models for Recovering Depth.- 5.1 Introduction.- 5.2 Space-Variant Filtering.- 5.3 Depth Recovery Using the Complex Spectrogram.- 5.4 The Pseudo-Wigner Distribution for Recovery of Depth.- 5.5 Imposing Smoothness Constraint.- 5.5.1 Regularized Solution Using the Complex Spectrogram..- 5.5.2 The Pseudo-Wigner Distribution and Regularized Solution.- 5.6 Experimental Results.- 5.7 Discussion.- 6 ML Estimation of Depth and Optimal Camera Settings.- 6.1 Introduction.- 6.2 Image and Observation Models.- 6.3 ML-Based Recovery of Depth.- 6.4 Computation of the Likelihood Function.- 6.5 Optimality of Camera Settings.- 6.5.1 The Cramer-Rao Bound.- 6.5.2 Optimality Criterion.- 6.6 Experimental Results.- 6.7 Discussion.- 7 Recursive Computation of Depth from Multiple Images.- 7.1 Introduction.- 7.2 Blur Identification from Multiple Images.- 7.3 Minimization by Steepest Descent.- 7.4 Recursive Algorithm for Computing the Likelihood Function.- 7.4.1 Single Observation.- 7.4.2 Two Observations.- 7.4.3 General Case of M Observations.- 7.5 Experimental Results.- 7.6 Discussion.- 8 MRF Model-Based Identification of Shift-Variant PSF.- 8.1 Introduction.- 8.2 A MAP-MRF Approach.- 8.3 The Posterior Distribution and Its Neighborhood.- 8.4 MAP Estimation by Simulated Annealing.- 8.5 Experimental Results.- 8.6 Discussion.- 9 Simultaneous Depth Recovery and Image Restoration.- 9.1 Introduction.- 9.2 Depth Recovery and Restoration using MRF Models.- 9.3 Locality of the Posterior Distribution.- 9.4 Parameter Estimation.- 9.5 Experimental Results.- 9.6 Discussion.- 10 Conclusions.- A Partial Derivatives of Various Quantities in CRB.- References.